It makes a difference because Intel is a more attractive and more consequential target for researchers. AMD's market share in servers is minuscule and even declining a bit as of 19Q1 (?), and modest but increasing nicely in notebooks and desktops https://news.ycombinator.com/item?id=19916279, while IBM's POWER and mainframe systems are expensive to very expensive to access.

ARM is actually a good target with a number of their newest designs using out-of-order speculative execution with Spectre vulnerabilities and their owning mobile space outside of notebooks, one of the newest even being vulnerable to Meltdown, but the significant headline worthy instances tend to come in much more locked down devices. Speed is also an issue, everything else being equal, the faster the chip, the faster data exfiltration proofs of concept will work.